If the pump is overheating and causing excessive drag on the engine, might be one place to check. See this on pressure washers before.
The engine tries to run further on choke, but still dies. This may or may not be due to fuel delivery, but easy enough to resolve. The carb should be replaced (usually inexpensive, < $20.00 for most) or totally disassembled and completely, thoroughly cleaned. Here's a link on how to
thoroughly clean a typical Honda carburetor:
How to Clean a Honda Carburetor
Unless you have super-rare model with a costly carb, it is generally faster/easier/less frustrating to just replace the whole carburetor.
Need to triple-check all the insulators, gaskets, and spacers and be 100% sure they are tear & damage free, and fitted correctly. It is easy to get one or more on upside down or backwards.
If you'll get me the full serial number off the side of the engine block, I can get you the part number and list price for a new carb and gaskets. The serial number will be in the form of "GXXX-1234567"